Riemann sums is an approximation of area using rectangles or trapezoids.
First of all, delta x is found by subtracting b from a and dividing by n subintervals.
LRAM is left hand approximation and the formula is:
delta x [f(a) + f( delta x +a) .... + f( delta x - b)]
Say you are asked to calculate the left Riemann Sum for -4x -5 on the interval [-3, -1] divided into 2 subintervals.
delta x would equal: -1+3 /2 = 2/2 = 1
1[ f(-3) + f(-3 +1)]
1[ f( -3) + f(-2)]
then plug into your equation
RRAM is right hand approximation and the formula is:
delta x [ f(a + delta x) + .... + f(b)]
so using the same example:
1[ f( -2) + f(-1)] and then plug into your equation
MRAM is to calculate the middle and the formula is:
delta x [ f(mid) + f(mid) + .... ]
To find midpoints, you would add the two numbers together then divide by two
In this problem the numbers would be: -3 , -2, -1
-3 + -2/ 2 = -5/2 and -2 + -1 / 2 = -3/2
so 1[f(-5/2) + f(-3/2)] and the plug in
Trapezoidal is different because instead of multiplying by delta x, you multiply by delta x/2 and you also have on more term then your number of subintervals.
The formula is : delta x/2 [f(a) + 2f(a + delta x) + 2f(a+ 2 delta x) + ....f(b)]
For this problem: 1/2 [ f(-3) + 2 f(-2) + f( -1)] and then plug in.
I am having trouble with:
1. Problems numbers 52-55 on our packet which give you an equations such as A(x) = the integral of b=x and a=-2 sin^3 (t) dt and you are asked to find A'(pi/2). I'm not exactly sure what they are asking for or where to even start.
2. Integrating trig functions raised to exponents such as the integral of (csc^6 x) (cot^2x)dx
3. The whole last page of the packet which asks to find the area of the region enclose by two equations between two x or y values.
This is kind of late so I'm not expecting answers before we turn our packets in, but answers will still be appreciated for future problems.
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